of Hydrogen in ThCoH

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of Hydrogen in ThCoH

₄

Samir F. Matar

CNRS, Universit´e de Bordeaux, ICMCB, 87 avenue du Docteur Albert Schweitzer, F-33608 Pessac, France

Reprint requests to Samir F. Matar. E-mail: matar@icmcb-bordeaux.cnrs.fr Z. Naturforsch.2011,66b,269 – 274; received December 3, 2010

We address the changes in the electronic structure brought by the insertion of hydrogen into ThCo leading to the experimentally observed ThCoH₄. Full geometry optimization positions the hydrogen in three sites stabilized in the expanded intermetallic matrix. From a Bader charge analysis, hydrogen is found to be in a narrow iono-covalent (∼ −0.6) to covalent (∼ −0.3) bonding which should enable site-selective desorption. The overall chemical picture shows a positively charged Th^δ⁺ with the negative charge redistributed over a complex anion{CoH4}^δ−withδ∼1.8. Nevertheless this charge transfer remains far from the one in the more ionic hydridocobaltate anion CoH₅⁴⁻in Mg₂CoH₅, due to the largely electropositive character of Mg.

Key words:ThCo Intermetallic, DFT, CrB Type, Hydrides, Bader Charge, Chemical Bonding

Introduction

Equiatomic (1 : 1) nickel-based binary intermetallic compounds such asANi withA= Y, Zr, Hf and rare earths (RE) [1–3] have been studied extensively both experimentally and theoretically in recent years mainly for their ability of absorbing hydrogen with up to three atoms per formula unit (fu) under mild conditions. On the other side, among the smaller number of cobalt 1 : 1 compounds, the hydrogen uptake within ThCo amounts to more than 4 atoms per fu (4.2) [4,5]. Such a result is interesting in as far as it resembles those in recent reports on a high hydrogen content inRENi leading toRENiH₄[2]. For ThCo, this leads to∼1.4 wt.-

% hydrogen instead of 3 wt.-% for hydrogenatedANi with the lighterAelements. Nevertheless, low weight percentages were also found in hydrogenated C15b pseudo-Laves hydrides such as REMgNiH₄ considered as candidates for on-board hydrogen storage [6].

Note that the use of the term “hydrogenated system”

rather than “hydride system” is intended to differenti- ate covalently bonded hydrogen within the intermetallic compound with respect to ionic hydrides such as those based on alkali and alkaline earth metals (cf.[3]

and refs. therein); this difference will be apparent from charge density analysis hereafter.

ThCo crystallizes in the orthorhombic space group Cmcm[7], similar toANi andANiHx[1,2]. To the best

0932–0776 / 11 / 0300–0269 $ 06.00 c2011 Verlag der Zeitschrift f¨ur Naturforschung, T ¨ubingen·http://znaturforsch.com

of our knowledge there are no reports on the structure and atomic positions for ThCoH₄, especially for hydrogen. In fact, for this purpose it is often required to replace hydrogen by deuterium for accurate determina- tions using neutron diffraction. It has been the aim of the present work to investigate the electronic structure of ThCo and ThCoH₄because the effects of hydrogen insertion such as the changes of the electronic structure and both the strength and character of the chemical bonding are important for an understanding of the properties of the material. These effects are modeled herein within the well established quantum mechani- cal density functional theory (DFT) framework [8,9].

Results and Discussion Computational framework

Within DFT, we use projector augmented wave (PAW) potentials within the VASP academic code [10,11], as built within the generalized gradient approximation (GGA) for an account of the effects of exchange and correlation [12]. Testing local density approximation (LDA) built potentials lead to largely smaller lattice parameters and volume magnitudes; the LDA which is constructed based on the electron gas distribution is known to be ‘over binding’. Firstly, an optimization of the atomic positions and lattice para-

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Cmcm ThCo [7] ThCo (calcd.) Bader ThCoH4 Bader Lattice parameters

a, ˚A 3.74 3.68 3.85

b, ˚A 10.88 10.86 11.70

c, ˚A 4.15 4.04 4.70

Volume, ˚A³/ 2 fu 84.43 80.73 105.86

Energy, eV −30.241 −60.589

Atomic positions

Th 4c(0,y,¹/⁴) 0, 0.136,¹/⁴ 0, 0.135,¹/⁴ +1 0, 0.131,¹/⁴ +1.8 Co 4c(0,y,¹/⁴) 0, 0.416,¹/⁴ 0, 0.407,¹/⁴ −1 0, 0.403,¹/⁴ +0.04

H1 4c(0,y,¹/⁴) 0, 0.913,¹/⁴ −0.58

H2 8f(0,y,z) 0, 0.306, 0.503 −0.47

H3 4b(0,¹/², 0) 0,¹/², 0 −0.31

Shortest dist., ˚A

Th–Co 2.86 2.76 3.06

Th–H1/Th–H2/Th–H3 2.81/2.59/2.73

Co–H1/Co–H2/Co–H3 1.93/1.63/1.64

Table 1. Geometry optimization results as compared to experiment data for ThCo and calculated values for ThCoH4.

meters is carried out. Then the equations of states (EOS) of ThCo and ThCoH₄ are obtained through energy-volume curves fitted with Birch EOS [13].

The calculated data are converged at an energy cut- off of 268 eV for all systems. Thek-point integration is carried out with a starting mesh of 4×4×4 up to 8×8×8 for best convergence and relaxation to zero strains. The Brillouin zone integrals are approximated using a specialk-point sampling following the Bl¨ochl algorithm [14].

An analysis of the charge density results is possi- ble by the approach of atoms in molecules and crys- tals (AIM) introduced by Bader [15] who developed an intuitive way of dividing molecules into atoms based purely on the electronic charge density. Typically in chemical systems, the charge density reaches a min- imum between atoms, and this is a natural region to separate atoms from each other. Such an analysis can be useful when trends between similar chemical systems are examined [16].

Also, the changes brought in by hydrogen into the density of states are addressed together with the character of the chemical bond between two atomic constituents based on the crystal orbital overlap popula- tion (COOP) [17]. In the plots, positive, negative and zero COOP magnitudes are indicative of bonding, antibonding, and nonbonding interactions, respectively.

Geometry optimization

Using the crystal data of Florioet al.[7] for ThCo, a geometry relaxation was carried out. Within space groupCmcm, there are 4 formula units (fu) per cell, but due to theC-centering only two fu are explicitly accounted for in the calculations. Table 1 shows the ex- perimental and calculated lattice parameters. The latter

Fig. 1 (color online). Sketch of the proposed ThCoH4struc- ture with coordination polyhedra of H1 (green, trigonal prism), H2 (red, tetrahedron) and H3 (yellow, flattened octa- hedron). Th and Co atoms are shown with smaller radii when taking part in the polyhedra.

are in fair agreement with the experiment especially for the atomic positions of Th while Co shows a change of theycoordinate. The volume is calculated slightly smaller, but the overall agreement gave confidence to investigate the hydrogenated system ThCoH₄.

For the hydrogenated ANi compounds in space groupCmcm[18], the uptake of 3 hydrogen atoms per fu results in an isotropic expansion of the cell, and hydrogen atoms are dispatched over two crystallograph-

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ically different sites, called hereafter H1 and H2.RE, Ni and H1 are at 4cpositions and H2 at 8f (cf. Ta- ble 1). H1 and H2 are then found in A₃Ni₂ trigonal bipyramids and A₃Ni tetrahedra, respectively. When extra hydrogen (H3) is inserted, resulting in theANiH₄ composition, Yaropolovet al.[2] proposed the occupa- tion of the 4b(0,¹/²,0) position whereby H3 is located in aA₄Ni₂ polyhedron. This is depicted in Fig. 1 for the presently studied system,i. e., withA= Th and Ni replaced by Co. These starting atomic positions were used to optimize the structure of ThCoH₄. The propo- sition of H3 at 4b(0,¹/²,0) was validatedversusanother ad hocposition, 4a(0,0,0), within preliminary calculations. The results led to a destabilization of the system by∼3 eV when hydrogen is at the 4aposition as compared to the 4bposition. Therefore we adopted the latter for H3 in the following calculations.

After geometry optimization, the orthorhombic symmetry was kept for the hydrogenated system within space groupCmcm. The calculated values of the lattice parameters and the internal atomic coordinates are given in Table 1. The volume increase upon hydro- genation of ThCo is∼25 %, a value within the range ofANiH₄, 23 – 25 % [2]. With respect to literature, the y_Th coordinate changes less than the y_Co and H1 and H2 coordinates. This is probably connected with the stronger bonding of H with Co rather than with Th resulting from larger distance to all three hydrogen sites, as shown in Table 1. The trend d(Co–H1)>d(Co–

H2/H3) was also observed in hydrogenated CeNi and YNi [19,20]. Regarding the energies, the hydrogen uptake stabilizes ThCo by−15.2 eV for 4H. This is further analyzed in the context of the binding energies below.

Energy – Volume EOS

In order to establish energy and relative stability trends, the equation of state (EOS) is needed, since one cannot rely solely on the quantities obtained from plain lattice optimizations, especially when compar- isons of energies and of volumes are required for different phases. The calculated total energy corresponds to the cohesion in the crystal, because the solution of the Kohn-Sham DFT equations gives the energy with respect to infinitely separated electrons and nuclei. As the zero of energy depends on the choice of the pseudo- potentials, the energy becomes arbitrary through its shifting, not scaling. However, the energy derivatives as well as the EOS remain unaltered. For this reason one needs to establish EOS’s from which the fit pa-

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(b)

Fig. 2 (color online). Energy versus volume curves for a) ThCo and b) ThCoH4 and fit results from Birch EOS shown in red. Lowχ²magnitudes indicate the goodness of fit value.

rameters are extracted for an assessment of the equilibrium values. This can be done from a set ofE(V) calculations for ThCo and ThCoH₄. The resulting curves shown in Fig. 2 have a quadratic variation which can be fitted with a Birch EOS to the 3^rdorder [13]:

E(V) =E_o(V_o) +9

8V_oB_o[(V_o/V)^2/3−1]² + 9

16Bo(B−4)Vo[(Vo/V)^2/3−1]³ (1) where E_o, V_o, B_o, and B are the equilibrium energy, the volume, the bulk modulus, and its pressure derivative, respectively. In both panels the goodness of fit of χ² ^is ∼10⁻⁶, providing reliability to the fit values. The B value amounts to ∼4, a magnitude usually observed [19,20]. The equilibrium volume of ThCo is close to the values calculated from geometry optimization and in better agreement with the experiment. For ThCoH₄, the equilibrium volume is slightly smaller than the optimized value. However,

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fit values which are zero pressure equilibrium quantities should be considered as more reliable for the rea- sons above. The bulk modulusB₀of ThCo amounts to

∼105 GPa. Compared to other 1 : 1 intermetallics, this value is larger than for CeNi (77 GPa) [19] and YNi (85 GPa) [20] while Ni and Co have the same magnitude of bulk modulus (180 GPa). The observed trend may follow from theAelements adjoined to them,i. e.

Ce (22 GPa), Y (41 GPa) and Th (54 GPa) [20]. A larger magnitude is obtained for ThCoH₄ despite the volume expansion, which could be related to the presence of metal-hydrogen bonding, especially Co–H, leading to an enhanced resistance of the system against compression and shearing. This is also observed for the hardening of carbides and borides.

Binding energies and charge density analysis

From the equilibrium energy results we examined the stability of ThCoH₄ using the following expres- sion per fu:E_stabil.= E(ThCoH₄) – E(ThCo) – 2 E(H₂).

While the first two terms of the right hand side of the equation are the equilibrium values obtained from the calculations, E(H₂) is derived from PAW-GGA calculations of H in a cube box with a large lattice spacing of 5 ˚A. The resulting energyE(H₂) =−6.59 eV is the total electronic energy. It includes twice the energy of monohydrogen (−0.95 eV from similar calculations), and it needs to be corrected by the zero point energy (ZPE). For H₂, ZPE amounts to∼0.28 eV as calculated by the same method [21]. The binding energy of H₂ is then−4.41 eV which is close in magnitude to the dissociation energy (inverse sign) of the molecule as obtained from fluorescence excitation spectroscopy:

∼36118 cm⁻¹,i. e.∼4.48 eV [22]. Then, with E(H₂) and the equilibrium energy values, the stabilization energy of hydrogen in ThCoH₄ (per 2 fu, using equilibrium values in the inserts) is:E_stabil.(H) = –60.64 – (−30.24) – 4(−6.59) = −4.04 eV for all 8H,i. e.

−0.5 eV per H. This value is close to the one computed for YNiH₄of∼ −0.56 eV per H [20].

This is further quantified by the charge density analysis within the atoms in molecules (AIM) theory [15]

presented above. In ThCo used as a reference for com- parison, we compute a charge transfer of∼1 electron from Th towards Co (Table 1, Bader columns). This follows the electronegativity order (Ξ) on the Pauling scale [23],i. e.a less electronegative Th (Ξ= 1.3) with respect to Co (Ξ = 1.9) and a larger electronegativity for hydrogen:Ξ (H) = 2.2. When H enters ThCo, the

charge on Th becomes larger (+1.8) and that on cobalt is not far from neutrality. The negative charges are carried by hydrogen atoms which are the nearest neighbors (nn) to cobalt, with different magnitudes rang- ing from−0.58 (H1) to−0.47 (H2) and−0.31 (H3).

This indicates a range of iono-covalently to covalently bonded hydrogen which follows the number of Co nearest neighbors and Th next nearest neighbors to hydrogen in the coordination spheres, i. e., Th3Co2, Th4Co2 and Th3Co, respectively. It can be seen that the difference of chemical behavior between the hydrogen atoms belonging to the two cobalt-containing polyhedra, namely Th3Co2 and Th4Co2, arises from the larger number of Th in the latter. This is different from ionic hydrides like MgH₂, where hydrogen is strongly bonded and carries a charge of∼ −1 (cf.[3] and refs.

therein). Hence, it can be suggested that in ThCoH₄ hydrogen should desorb site-selectively from the intermetallic matrix, starting with the least ionically bonded H3, such as by the effect of temperature. The overall chemical picture is close to a complex-type system: Th^δ⁺(CoH₄)^δ⁻withδ ∼1.8. Nevertheless, this charge transfer remains far from that in the ionic complex hydridocobaltate anion (CoH₅)⁴⁻, in Mg₂CoH₅ which follows the 18-electron rule [24]. This is due to the largely electropositive character of Mg leading to a total charge transfer of 4 (2×2) electrons to CoH₅.

Density of states and chemical bonding

The site-projected density of states (PDOS) is shown in Fig. 3 for ThCo and ThCoH₄. Along the xaxis the energy reference is taken with respect to the Fermi levelE_Fbecause both systems have a finite, al- beit small, density of states at the top of the valence band (VB), with contributions arising from Th (d, f) and Co (d) states. The VB is mainly dominated by Co (d) states centered belowE_Fdue to Co having its 3d subshell largely populated. On the contrary, the con- duction band (CB, aboveE_F) is dominated by Th (5f) states. Nevertheless, itinerant states arising from Th (6d) are found within the VB; they are involved with the bonding involving Co valence states.

The similar peak shapes observed through the lower part of the VB indicate a quantum mixing between the metal constituents in the range{−6,−3 eV} for ThCo and {−3 eV, E_F} for ThCoH₄. In the latter, a narrowing for both Co and Th energy intervals within the VB is observed, accompanied by more localized and intense peaks, especially for cobalt. These are the

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(a)

(b)

Fig. 3 (color online). Site-projected density of states for a) ThCo and b) ThCoH4.

respective consequences of the volume increase leading to larger interatomic separations and PDOS peak localization and of the extra electrons brought by the four additional hydrogen atoms. The novel feature of the PDOS with respect to ThCo is the emergence of extra states created in the lower part of the VB,i. e.

between−4 eV and −10 eV within which hydrogen binds with the metallic constituents, mainly Co. This is also evident from the presence of Co and Th PDOS peaks just belowE_Fin Fig. 3b, involving the bonding of Co and Thdorbitals with H as detailed below.

The chemical bonding is discussed based on the COOP plots for metal-metal and metal-H interactions in Fig. 4. For a clear presentation of bonding strengths of the Th–H and Co–H interactions regroup all three

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(b)

Fig. 4 (color online). Chemical bonding for pair interactions in a) ThCo and b) ThCoH4.

sites H1, H2 and H3. In ThCo (Fig. 4a), the Th–Co interaction is stronger than Th–Th and Co–Co interactions. It is of bonding character over the whole VB energy range. This is also observed for the weaker Th–Th interactions. On the contrary, Co–Co shows bonding and antibonding interactions within the VB due to the high filling of Co (d) orbitals. The antibonding COOP appears in the CB at 1 eV for Th–Co and 3 eV for Th–

Th. The energy order for the occurrence of antibonding COOP in ThCo is Co–Co at−1 eV, Th–Co at 1 eV and Th–Th at 3 eV. It is concomitant with the number of electrons involved in the interaction: the more electrons are involved, the earlier the antibonding COOPs appear.

In ThCoH₄(Fig. 4b), the Th–Co bonding intensity is reduced with respect to Fig. 4a, it extends over a wider

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energy range with a small intensity COOP centered at−7 eV, and it is separated from the major COOP con- tribution at−2 eV. Th–Co bonding remains dominant with respect to both Th–H and Co–H whose COOPs follow the same shape as Th–Co, signaling covalent- like interactions. Contrary to Fig. 4a, Th–Co antibonding COOPs in Fig. 4b are now observed below E_F. With respect to ThCo, the addition of four hydrogen atoms bringing four extra electrons leads to a higher energy shift ofE_F as schematized by the bold verti- cal line at∼1 eV in Fig. 4a. The enhancement of the antibonding COOP belowE_F, signaling a less bonded Th–Co metal sublattice, is due to the larger Th–Co distance (Table 1) and to the involvement of some of the Th and Co electrons with hydrogen bonding. As in the PDOS plots, the COOP present a more localized feature due to the lager volume of the hydrogenated compound (Table 1). Although both metal-hydrogen interactions are bonding, the Th–H COOP intensity is much smaller than that of Co–H, being observed below the Th–Co COOP peaks at∼ −2 eV. This supports the discussion above conclusion regarding the chemical structure. Both possess a COOP massif just below

E_F, corresponding to the extra PDOS peak developed in ThCoH₄(Fig. 3b).

Conclusion

The aim of this work using DFT electronic structure methods was to address the changes brought by the insertion of hydrogen into ThCo leading to the for- mation of the experimentally observed ThCoH₄. Full geometry optimizations lead to a positioning of hydrogen atoms within the intermetallic matrix. The energy volume equations of states for the intermetallic and the hydrogenated compound indicate its stabilization. The analyses of the DOS show large changes within the valence band with new states introduced by hydrogen into the lower part of the valence band and a larger localization of Th and Co partial DOS. From the chemical bonding analysis, the major bonding is observed for Co–H with antibonding Th–H. Bader charge analysis shows that hydrogen exhibits iono-covalent to covalent behavior. The overall chemical picture shows a positively charged Th^δ⁺and a complex hydridocobaltate [CoH₄]^δ⁻ withδ = 1.8, less ionic than in Mg-based hydridocobaltate.

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